Antideuteron and deuteron production in
midcentral Pb+Pb collisions at 158A GeV
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Anticic, T. et al. “Antideuteron and Deuteron Production in
Midcentral Pb+Pb Collisions at 158A GeV.” Physical Review C 85.4
(2012). ©2012 American Physical Society
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http://dx.doi.org/10.1103/PhysRevC.85.044913
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Final published version
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http://hdl.handle.net/1721.1/71681
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PHYSICAL REVIEW C 85, 044913 (2012)
Antideuteron and deuteron production in midcentral Pb
+ Pb collisions at 158A GeV
T. Anticic,22B. Baatar,8D. Barna,4J. Bartke,6H. Beck,9L. Betev,10H. Białkowska,19C. Blume,9M. Bogusz,21B. Boimska,19 J. Book,9M. Botje,1P. Bunˇci´c,10T. Cetner,21P. Christakoglou,1P. Chung,18O. Chvala,14J. G. Cramer,15V. Eckardt,13
Z. Fodor,4P. Foka,7V. Friese,7M. Ga´zdzicki,9,11K. Grebieszkow,21C. H¨ohne,7K. Kadija,22A. Karev,10V. I. Kolesnikov,8
M. Kowalski,6D. Kresan,7A. Laszlo,4R. Lacey,18M. van Leeuwen,1M. Ma´ckowiak-Pawłowska,21M. Makariev,17
A. I. Malakhov,8M. Mateev,16G. L. Melkumov,8M. Mitrovski,9St. Mr´owczy´nski,11V. Nicolic,22G. P´alla,4
A. D. Panagiotou,2W. Peryt,21J. Pluta,21D. Prindle,15F. P¨uhlhofer,12R. Renfordt,9C. Roland,5G. Roland,5M. Rybczy´nski,1 A. Rybicki,6A. Sandoval,7N. Schmitz,13T. Schuster,9P. Seyboth,13F. Sikl´er,4E. Skrzypczak,20M. Slodkowski,21
G. Stefanek,11R. Stock,9H. Str¨obele,9T. Susa,22M. Szuba,21M. Utvi´c,9D. Varga,3M. Vassiliou,2G. I. Veres,4
G. Vesztergombi,4D. Vrani´c,7Z. Włodarczyk,11and A. Wojtaszek-Szwar´c11
(NA49 Collaboration)
1NIKHEF, Amsterdam, Netherlands
2Department of Physics, University of Athens, Athens, Greece 3E¨otv¨os Lor´ant University, Budapest, Hungary
4KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary 5MIT, Cambridge, Massachusetts, USA
6H. Niewodnicza´nski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 7GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, Darmstadt, Germany
8Joint Institute for Nuclear Research, Dubna, Russia 9Fachbereich Physik der Universit¨at, Frankfurt, Germany
10CERN, Geneva, Switzerland
11Institute of Physics, Jan Kochanowski University, Kielce, Poland 12Fachbereich Physik der Universit¨at, Marburg, Germany
13Max-Planck-Institut f¨ur Physik, Munich, Germany
14Institute of Particle and Nuclear Physics, Charles University, Prague, Czech Republic 15Nuclear Physics Laboratory, University of Washington, Seattle, Washington, USA 16Atomic Physics Department, Sofia University St. Kliment Ohridski, Sofia, Bulgaria
17Institute for Nuclear Research and Nuclear Energy, BAS, Sofia, Bulgaria 18Department of Chemistry, Stony Brook University (SUNYSB), Stony Brook, New York, USA
19National Center for Nuclear Research, Warsaw, Poland
20Institute for Experimental Physics, University of Warsaw, Warsaw, Poland 21Faculty of Physics, Warsaw University of Technology, Warsaw, Poland
22Rudjer Boskovic Institute, Zagreb, Croatia
(Received 12 November 2011; published 10 April 2012)
Production of deuterons and antideuterons was studied by the NA49 experiment in the 23.5% most central Pb+ Pb collisions at the top CERN Super Proton Synchroton (SPS) energy of √sN N = 17.3 GeV. Invariant yields for d and d were measured as a function of centrality in the center-of-mass rapidity range−1.2 < y < −0.6. Results for d(d) together with previously published p(p) measurements are discussed in the context of the coalescence model. The coalescence parameters B2were deduced as a function of transverse momentum ptand
collision centrality.
DOI:10.1103/PhysRevC.85.044913 PACS number(s): 25.75.Dw
I. INTRODUCTION
Studies of antideuteron and deuteron production in heavy-ion collisheavy-ions are attractive for many reasons. Enhanced antimatter production in central nucleus-nucleus collisions relative to p+ p was proposed as one of the experimental signatures for formation of a new state of strongly interacting nuclear matter—the quark-gluon plasma [1–3]. If antibaryon abundances are not in equilibrium or not strongly affected by annihilation after chemical freeze-out, some of the initial enhancement may survive till the final stage of the colli-sion process. However, at CERN Super Proton Synchroton (SPS) energies baryon rich nuclear matter is created at high
temperatures (μB ≈ 250 MeV and T ≈ 160 MeV in central
Pb+ Pb collisions at 158A GeV [4]). In a hadronic medium of such temperature and baryon density, reaction rates involving antibaryons will be high due to annihilation and multipion fusion processes [5–7]. Thus any antimatter enhancement from the partonic phase or its transition to the hadronic phase is likely to survive only if freeze-out occurs right after the phase transition.
At the late stage of the fireball evolution, when the hadronic matter is diluted enough such that secondary inelastic colli-sions cease, the observed clusters are formed from nucleons. The process of nucleosynthesis in strongly interacting systems
044913-1
heated to more than 100 MeV was extensively studied over the past years for species ranging from A= 2 to A = 7 [8–13]. Recently, the formation of (anti)hypernuclei was observed in Au+ Au collisions by the E864 experiment at AGS energies [14] and by the STAR collaboration at RHIC [15].
In a simplified coalescence approach [16,17], (anti)nucleon bound states are formed from (anti)nucleons which are close in momentum and configuration space. Their production is usually characterized by the coalescence factor BA which
relates the invariant yield of a cluster of size A to the Ath power of the proton yield. The B2parameter for deuterons was
found to be approximately constant in heavy-ion collisions at beam energies below 1A GeV as well as in all proton-induced reactions. However, at higher collision energies (more than several GeV per nucleon) the diameter of the source created in central collisions is much larger than the deuteron size due to expansion of the reaction zone, and the cluster production process becomes sensitive to the details of the phase-space distribution of the constituents. In particular, a strong collective radial flow (the average transverse velocity is about 0.5c at SPS energies [18]) produces correlations between the production point in space-time and the momentum of the clusters. Thus, an interplay between the flow velocity profile and the nucleon density distribution may result in different shapes of transverse momentum spectra for composites and single nucleons [19]. A comparative analysis of the production of clusters made of nucleons and antinucleons might therefore provide insight into the details of the fireball evolution and the nucleon phase-space distribution at kinetic freeze-out. The production rate of composites should depend on the spatial distribution of their constituents. If the p suffer from annihilation in the dense baryonic matter, this could therefore be reflected in the impact parameter dependence of the d yield [20]. Moreover, because of the additional annihilation cross section, d are expected to decouple from their source at much lower hadron density than d and therefore their freeze-out volume is expected to be larger. In summary, the study of d and d production provides an alternate method for extracting information about the source size [21,22] which is complementary to the femtoscopy approach.
Recently, NA49 reported [23] on p production at midra-pidity in centrality selected Pb+ Pb collisions at 158A GeV. In the following we extended this study of antimatter to the investigation of heavier systems. This paper reports our measurement of d and d invariant yields around midrapidity in the same reaction.
The paper is organized as follows. The next section gives an overview of the NA49 experimental setup. Details of the data analysis procedure are described in Sec.III. In Sec. IV
we present and discuss the results on d and d production in midcentral Pb+ Pb collisions. A summary is given in the last section.
II. EXPERIMENTAL SETUP
The NA49 apparatus was designed as a large acceptance magnetic spectrometer to study nucleus-nucleus collisions in the SPS energy range. The NA49 setup covers about 50% of
the final state phase space for Pb+ Pb reactions at a beam energy of 158A GeV. The detector provides precise tracking and robust particle identification. A full description of the apparatus components can be found in Ref. [24].
The primary lead beam was extracted from the SPS and delivered to NA49 through the H2 beam line in the SPS North Area. The intensity of the beam (delivered in spills 4.8 s long) was typically 105/s. The beam was defined within
the experiment by a set of Cherenkov and scintillation counters placed along 35 m of the beam path upstream from the nominal target position. The transverse diameter of the beam spot on the target, as measured by three multiwire proportional beam po-sition detectors (BPDs), was about 1 mm. The target was a lead foil of 337 mg/cm2thickness (1.5% of a Pb interaction length).
The interaction trigger required a valid beam signal plus a collision centrality tag based on the measurement of projectile spectator energy registered in the zero-degree calorimeter VCAL which was placed 23 m downstream of the target.
Charged reaction products originating from the interaction vertex are recorded by four gas time projection chambers (TPCs). Two vertex TPCs (VTPC), serving mainly for momen-tum analysis, are located inside two superconducting dipole magnets, which provide a magnetic field with a total bending power of about 9 Tm. The two main TPCs (MTPC), with about 27 m3gas volume each, are positioned behind the magnets on
each side of the beam line. These TPCs are optimized for energy loss (dE/dx) measurements with a precision of 4% for minimum ionizing particles (mip).
Two time-of-flight (TOF) arrays (walls), positioned behind the MTPCs at≈14 m from the interaction vertex, are the main detector systems used in this analysis for the identification of charged hadrons of momenta up to 10 GeV/c. The TOF setup provides rapidity coverage of about 0.8 units in the mid-rapidity region and transverse momentum coverage up to pt=
2.5 GeV/c. Each wall consists of 891 pixels made of 2.5 cm thick plastic scintillators with transverse dimensions of 6, 7 and 8 cm (horizontal) by 3.4 cm (vertical). Each pixel is viewed by one phototube of 1.4 inch diameter glued to the side of the pixel. The phototube outputs (typically 1.5 Volts high for a charge=1 mip passing through the pixel) are divided into two equal parts and digitized by TDCs and ADCs for time-of-flight and energy loss measurements, respectively. The least count of the FASTBUS LeCroy TDCs was set to 25 ps. Pixels are assembled in groups of 11 (as stacks in the vertical direction) in light-protected cassettes.
A 0.5 mm thick quartz Cherenkov counter S1placed 34 m
upstream of the target provided the common start signals and the gates to the TDCs and ADCs, respectively. For a beam of lead nuclei S1has an intrinsic time resolution about 30 ps.
The overall time resolution achieved with the TOF system was σ ≈ 60 ps and allows for a 5σ p/d separation up to a momentum of p= 10 GeV/c.
III. DATA ANALYSIS A. Data sets
A high statistics sample of Pb+ Pb collisions at beam energy of 158A GeV was collected during the year 2000
ANTIDEUTERON AND DEUTERON PRODUCTION IN MID- . . . PHYSICAL REVIEW C 85, 044913 (2012) TABLE I. Summary of the data sets used in the analysis. The
number of events employed are given together with the fraction of the total cross-section (in percent) and corresponding average number of wounded nucleonsNW per event derived from the VENUS model.
Centrality NW Nevents
0–23.5% 265 2.40× 106
0–12.5% 315 1.24× 106
12.5–23.5% 211 1.16× 106
run period. A total of 2.4× 106 events were recorded with
an online event trigger selecting the 23.5% most central collisions.
To study the centrality dependence of the d and d yields the data set was divided into two centrality classes (see Table
Ifor detail). For each centrality selection, the corresponding average number of wounded nucleons NW as well as the
percentage of the total cross section were obtained from the Glauber model approach using a simulation with the VENUS event generator [25,26].
B. Time-of-flight reconstruction
The analysis procedure starts with the calibration of all TOF pixels: time-zero offsets T0, ADC gains, and pedestals were
determined. All reconstructed tracks in the TPCs with assigned momentum were extrapolated toward the TOF detectors and all possible associations between the track extrapolations and the calibrated TOF hits were found. For each TOF hit the raw TDC count was then corrected for the light propagation time in the scintillator according to the position of the point from which the light originated, and for the amplitude-dependent time-walk effect in the discriminator. The correction was as large as 50 ps/cm and 30 ps for the light propagation time and time-walk effect, respectively. Finally, an event-by-event global time offset (≈40–50 ps on average) was determined as the mean of the distribution of the differences between the measured and calculated arrival time for pions selected by their energy loss dE/dx in the TPCs (15 to 30 π ’s per wall in an event depending on the collision centrality). The achieved overall time resolution of the TOF system was about 60 ps.
The squared mass m2was calculated from the reconstructed momentum p, the flight path to the TOF detector l and the measured time-of-flight t as m2= p 2 c2 c2t2 l2 − 1 , (1)
where c denotes the speed of light.
C. Event and track selection
In the following we discuss the event selection criteria as well as the track and TOF hit quality cuts which were applied during the analysis. In order to eliminate the background from nontarget interactions an offline cut on the vertex z coordinate along the beam line was imposed. The difference between the z position reconstructed from tracks and the nominal
(survey) target position was required to be less than 1 cm (±4σ deviation, with σ being the rms of the vertex z distri-bution). The fraction of events rejected by this cut was about 0.5%.
Track candidates were required to have a valid momentum fit result and dE/dx measurement. In order to reduce the contamination by background tracks from secondary interactions in the material or decays inside the TPC, the following track quality criteria were applied:
(i) Tracks were accepted if they had points in the MTPC and in at least one of the VTPCs, and the length of the MTPC track segment was longer than 1.5 m.
(ii) Both vertical and horizontal deviations from the vertex position, after back extrapolation to the z position of the target, were required to be less than 1 cm.
An additional set of quality cuts was imposed to reject those TOF hits that have poorly reconstructed time of flight: (i) Candidates were rejected if two or more tracks in the event
hit the same scintillator.
(ii) A distance greater than 1 mm from the pixel’s edges was required for the position of a TOF hit to account for mismatches between TPC tracks and TOF signals due to multiple scattering and TPC-TOF misalignment.
(iii) A cut on the energy deposited in a scintillator was applied to reduce background under the (anti)deuteron mass peak due to false TOF hits and interactions of γ s associated to the interactions. The ADC value normalized to minimum ionizing particles was required to be within 0.8 < ADC/ADCmip<1.4.
The fraction of the TOF hits remaining after all the quality cuts was found to be 67%.
D. Identification of deuterons and antideuterons
Particle identification is done in two steps by combining measurements of time of flight from the TOF detector and dE/dx from the MTPCs. First, the allowed values of dE/dx were limited to
dE/dx < dE/dxBB(p)+ kσ (p)
where dE/dxBB(p) is the most probable value as taken
from a momentum dependent parametrization of the Bethe-Bloch curve for deuterons, and σ (p) is the corresponding resolution in dE/dx. The parameter k was set to 3 and 2 for d and d, respectively. As illustrated in Fig. 1 (left panel) for the momentum bin 7 < p < 8 GeV/c such a cut reduces the contribution of pions and kaons to the d (d). The resulting m2distributions for positively and negatively charged particles after applying the previously described quality and dE/dx PID cuts show clear d and d peaks (Fig. 1, right panel). The entire track sample of d(d) was divided into transverse momentum bins of 0.15 GeV/c width; the three highest pt bins were combined into a wider one because of
lack of statistics. In each pt bin candidates are selected by
a±3σ window in m2 around the nominal position. The raw
yields were determined by summing the histogram bin contents within the mass window. The background contamination under 044913-3
1 1.2 1.4 1.6 0 2.5 m2 (GeV2/c4)
dE/dx (arb. units)
d p (a) 1 10 102 103 2 4 d d m2 (GeV2/c4) (b)
FIG. 1. (Color online) (a) dE/dx versus m2 for positively
charged particles in the momentum interval 7 < p < 8 GeV/c. The dashed ellipse illustrates the region populated by deuterons; the PID upper-limit dE/dx cut is indicated by the horizontal line. (b) m2
distributions for both charges around the m2
d position for momenta
from 4 to 10 GeV/c [dE/dx PID cut for d(d) was applied]. The arrow indicates the nominal m2position for d(d).
the d (d) peak was evaluated by fitting the m2distribution to
a sum of a Gaussian signal and an exponential background. Figure 2 shows mass squared distributions along with the combined (Gauss + exponential) fits for d for three pt bins.
The background contamination is weakly dependent on ptand
amounts to less than 3% for deuterons, but reaches≈ 45% for d. The statistical error of the raw d yields was calculated as √
N=Nd+ Nbkg, where Nd and Nbkgare the number of d
and background counts, respectively.
E. Corrections
The raw yields were weighted by correction factors which account for the geometrical acceptance and for the losses due to the applied track quality and dE/dx PID cut.
Correction factors for the limited geometrical coverage of the detector system were obtained from a GEANT-based Monte Carlo simulation. Figure 3 shows the NA49 TOF acceptance for d(d) in terms of transverse momentum pt
and center-of-mass rapidity y. The bin size was taken to be y= 0.1 by pt = 25 MeV/c, and all the bins at the edges of
the acceptance were rejected to avoid a very large correction factor. The acceptance drops down to about 6% at pt >
0.6 GeV/c. Monte Carlo studies with simulated tracks em-bedded into real data showed that the tracking reconstruction efficiency in the phase-space region covered by the TOF detector is above 98%. All remaining corrections were de-termined from the data in bins of pt. For each centrality bin
the corrections for multihits were obtained by determining
0 5 10 (a) dn/dm 2 0 5 10 (b) 0 5 10 2.5 3 3.5 4 4.5 (c) m2 (GeV2/c4)
FIG. 2. Mass-squared distributions of d for rapidity−1.2 < y < −0.6 in several transverse momentum bins: (a) 0 < pt <0.3 GeV/c,
(b) 0.3 < pt<0.45 GeV/c, (c) 0.45 < pt <0.6 GeV/c. Solid lines
represent fits of a sum of a Gaussian signal and an exponential background.
the fraction of tracks rejected by the requirement that only a single one hits a scintillator. This correction shows less than 3% variation with centrality and is on average 11% and 8% for the 0–12.5% and 12.5–23.5% most central events, respectively. The losses due to the geometrical fiducial cut (1 mm edge cut) were determined averaged over all centralities. This correction accounts for about 9% losses. The corrections (about 15%) due to the pulse height constraint (0.8 < ADC/ADCmip<1.4)
were determined for the deuteron sample and applied for both d and d. The corrections for the losses due to the DCA cut (≈2%) were also determined from the DCA distributions of the deuteron candidates.
y −1.2 −1 −0.8 (GeV/c) t p 0 0.2 0.4 0.6 0.8 acceptance 0 0.5 1
FIG. 3. (Color online) Geometrical TOF acceptance as a function of rapidity y and transverse momentum pt for d at 158A GeV.
ANTIDEUTERON AND DEUTERON PRODUCTION IN MID- . . . PHYSICAL REVIEW C 85, 044913 (2012)
F. Systematic errors
The systematic errors of the d and d yields originate mainly from the uncertainties of particle identification and efficiency correction factors. In general, each particular contribution to the overall systematic error was estimated by varying the characteristic selection criteria, i.e., by loosening some cut or making it tighter. The contributions of the following selection criteria were studied: the dE/dx identification cut, the pulse height and geometrical cuts for selecting TOF hits and the DCA cut for selecting tracks. The uncertainty arising from the PID procedure for d (including background subtraction) introduces a systematic error of the order of 13%. The DCA cut contributed≈5% to the overall systematic error. The error associated with the TOF efficiency correction for d was found to be 9%.
The overall systematic error, obtained as the quadratic sum of all contributions, was estimated to be 17% for d and 10% for d.
IV. RESULTS AND DISCUSSION A. Transverse momentum distributions
Figures4(a)and4(b)shows the invariant yields of d and d for centrality selected Pb+ Pb collisions as a function of transverse momentum pt. The yields are averaged over
the center-of-mass rapidity interval −1.2 < y < −0.6. The data for the most central bin are shown to scale, while each successive distribution was divided by an additional factor of ten for clarity of presentation. We have also analyzed p and p yields in the same centrality selected event samples. A detailed description of the analysis procedure for (anti)protons can be found elsewhere [23]. The invariant distributions for p and p measured in the rapidity interval−0.5 < y < −0.1 are shown in Figs. 4(c)and4(d). The yields agree with the previously published data [23] within 12%, the observed difference is mainly due to feed-down corrections from weak decays which are now based on the recent experimental data on () production from the NA49 experiment [27,28]. Numerical values of the transverse momentum spectra are given in TablesIV–VIIof the Appendix.
Calculations using the microscopic transport model UrQMD [29] suggest that because of annihilation in dense baryon matter a considerable difference between the pt
distributions of anticlusters compared to those of clusters is expected. If annihilation of antimatter in the fireball medium affects d production, then one would expect d losses to be larger at midrapidity and at low pt[30], resulting in a hardening
of the pt spectra of d compared to those for d. On the other
hand, the NA49 measurements of midrapidity p(p) spectra [23] show little difference between transverse distributions of pand p for all centralities, leading to the conclusion that the pt dependence (if any) of annihilation losses for antiprotons
is small at 158A GeV. A similar behavior is also observed for the s and anti-s [28].
The experimental deuteron distributions were fitted to an exponential function in mt[shown by curves in Fig.4(a)]
1 pt d2N dptdy = dN/dy T(m+ T )exp −mt− m T , (2) 10-4 10-3 10 -2 10-1 1 x 1 x 0.1 x 0.01 d (a) d 2 N/(p t dp t dy) (GeV -2 c 2 ) 10-6 10-5 10-4 10-3 x 1 x 0.1 x 0.01 d (b) 10-3 10-2 10-1 1 10 102 0 1 2 3 (c) p x 1 x 0.1 x 0.01 pt (GeV/c) d 2 N/(p t dp t dy) (GeV -2 c 2 ) 10-3 10-2 10-1 1 10 0 0.5 1 1.5 2 x 1 x 0.1 x 0.01 p (d) pt (GeV/c)
FIG. 4. (Color online) The transverse momentum spectra of deuterons (a), antideuterons (b), protons (c), and antiprotons (d) in centrality selected Pb+ Pb collisions at 158A GeV. Only statistical errors are shown. The curves show exponential fits to the data using Eq.(2). Results for the 0–12.5% most central collisions are shown to scale, results for the centrality intervals 12.5–23.5% and 0–23.5% are divided by factors 10 and 102, respectively.
where dN/dy and T are two fit parameters, mt =
p2
t + m2
is the transverse mass and m the deuteron rest mass.
The small available statistics and resulting limited ptrange
for d data makes the determination of the slope parameters for dless accurate. Thus only the dN/dy parameter was allowed to vary when the d spectra were fitted and merely a qualitative comparison of the shape of the spectra is possible. As one can see in Fig. 4(b), the fits of d spectra with slope parameters fixed to the values obtained from the d distributions from the same collision centrality [Fig.4(a)] appear to describe the d data well. In Fig.5, the d/d ratio for the 0–23% centrality bin is plotted as a function of pt. The ratio shows little variation
with ptwithin the errors. A fit with a constant yields an overall
d/dratio of (2.2± 0.2) × 10−3. Since no difference in shapes of d and d spectra was observed, a likely conclusion is that the dynamical properties of the formation process are the same for d and d production. There is also no indication of extra reduction of the d yield at low ptdue to annihilation.
The fit parameters dN/dy for the d and d spectra in different centrality bins are tabulated in TableII. The fraction of the yield integrated using Eq.(2)over the unmeasured pt
range is≈7% for d and 55% for d.
The slope parameter T for deuterons is 406± 12 MeV and 391± 12 MeV for the 0–12.5% and 12.5–23.5% most central collisions, respectively. It tends to increase with increasing centrality indicating increase of collective transverse flow. In Ref. [13] we reported yields and slopes for deuterons from the 1996 minimum bias data set of Pb+ Pb collisions at 158A GeV, subdivided into six centrality bins. These measurements for deuterons were obtained in the rapidity 044913-5
0.001 0.002 0.003 0.004 0.005 0 0.2 0.4 0.6 0.8 1 centrality: 0-23.5% pt (GeV/c) d/d ratio
FIG. 5. d/d ratio as a function of pt in 0–23.5% central Pb+ Pb
collisions at 158A GeV. The dashed line shows a fit to a constant.
range −0.9 < y < −0.4, and only tracks with px >0 were
used. Taking into account the different rapidity intervals for both measurements (an increase of 15% in dN/dy and a decrease of about 5% in T is expected when going from y= −0.65 to y = −0.9), the overall agreement of the present results with our previously published data is satisfactory.
The invariant pt spectra of d(d) are harder than those of
p(p) [23] (typical Tp ≈ 290–300 MeV). As was pointed out in
[19,22], the characteristic change of the slope with the particle mass is sensitive to the interplay between the density and flow velocity profiles in the source at freeze-out. The observed increase of the inverse slope parameter T of about 30% for d can, for instance, be explained by a combination of a box-like density profile and a linear increase∝ r/R of the transverse flow velocity with distance r from the center of the fireball of radius R, or by a Gaussian density profile and an increase of the flow velocity∝ (r/R)α with α in the range 0.5–1.0. (see
Fig.1in [19]). Future results on3He and triton production [31]
are expected to provide additional constraints.
B. Rapidity distributions and total yields
Yields of d and d as a function of rapidity for the 23.5% most central Pb+ Pb collisions are shown in Fig.6. There is a difference between the shapes of the rapidity spectra for d and d. The observed distinction can be traced back to the TABLE II. dN/dy for d and d obtained from fits with Eq.(2)
in centrality selected Pb+ Pb collisions at 158A GeV in the rapidity interval−1.2 < y < −0.6. Errors are statistical only.
Centrality Deuterons Antideuterons 0–12.5% 0.33± 0.02 (8.1± 1.1) × 10−4 12.5–23.5% 0.25± 0.02 (5.6± 1.0) × 10−4 0–23.5% 0.3± 0.01 (6.9± 1.0) × 10−4 0.5 1 1.5 -2 0 2 d x 1000 d y dN/dy
FIG. 6. (Color online) Rapidity distributions for d (squares) and
d (circles) produced in the 23.5% most central Pb+ Pb collisions at 158A GeV. The solid symbols indicate the measured data points, the open symbols are reflected at midrapidity. The curves represent the results of different fits motivated by a coalescence approach (see text).
longitudinal distributions of their constituents. Data on p and pproduction in centrality selected Pb+ Pb collisions at 158A GeV were recently published by NA49 [32]. For collisions of all centralities, the proton rapidity distributions have a dip at midrapidity in contrast to the peak observed for antiprotons. Since the abundance of (anti)clusters (of mass number A) is proportional to the (anti)nucleon phase-space density raised to Ath power, the effect of the difference in the shapes of the rapidity distributions is even more pronounced for the composites.
In Fig. 6 two Gaussian distributions are plotted for d. The dotted line represents the simplest expectation from the coalescence model, namely a Gaussian with a width which is smaller by a factor of√2 than that for antiprotons for the centrality class 0–23 % [32]. The integral of this distribution is equal to that of the second Gaussian (shown by the dashed line), whose parameters, i.e. the width and total yield were calculated based on the measured points (two unknown parameters and only two measured points). The calculated parameters were found to be 2.4× 10−3for the 4π yield and 0.95 for the width. The calculated width is close to that observed for antiprotons (σp ≈ 0.93–1.03) in the centrality range under study [32].
In the case of d production the estimate of the 4π yield is not well constrained by our measurements. Nevertheless, we used the coalescence model to obtain estimates based on parametrizations fitted to the proton rapidity spectrum [32] in the region covered by the NA49 data. First we fitted a parabolic rapidity dependence to the proton yield. The d distribution predicted by the coalescence model (see dash-dotted curve in Fig. 6) was then normalised to the d measurements and
ANTIDEUTERON AND DEUTERON PRODUCTION IN MID- . . . PHYSICAL REVIEW C 85, 044913 (2012) integrated out to beam rapidity ybeamresulting in an estimate
of the total yield for d of 3.5± 0.4. However, the rapidity distribution of protons may eventually decrease toward ybeam
as observed for the lower beam energy data in Ref. [32]. As an alternative we therefore fitted the proton rapidity distribution by three Gaussian distributions, one centered at y= 0 and a pair displaced symmetrically with respect to y= 0, using the additional constraint that the fit function should rapidly go to zero beyond ybeam. This procedure also results in a
good fit of the proton rapidity distribution in the region of the measurements. The alternative prediction of the coalescence model is shown by the solid curve in Fig.6and results in an estimate of the total d yield of 1.75± 0.18.
Rough estimates for the total (anti)cluster yields were made in the framework of a statistical hadron gas model (HGM) [33]. A total yield of 2.5 and 4.6× 10−3was predicted in the 5% most central Pb+ Pb collisions at 158A GeV for d and d, respectively. Assuming the yield of clusters to scale with the number of wounded nucleons (NW changes by a factor
of about 1.4 from 5% to 23.5% centrality of collisions), the difference between data and the HGM estimates is below 40% for both d and d.
C. Centrality dependence of d and d yields
In Fig.7the invariant yield of d and d normalized to the number of wounded nucleonsNW is plotted as a function of
NW. The previously published NA49 results for deuterons
from the year 1996 minimum bias data set [13] (blue circles) are also shown. Within the experimental errors, the centrality dependence (if any) of the d yield perNW appears to be weak
in midcentral Pb+ Pb collisions. Also the normalized yield
0.05 0.1 0.15 0.2 x 10-2 100 200 300 400 d (y=-0.6, min.bias 1996) d (y=-0.9, mid.central 2000) d (y=-0.9, mid.central 2000) x 100 <Nw> (dn/dy)/ <N w >
FIG. 7. (Color online) dN/dy divided by the average number of wounded nucleons NW for d and d for Pb + Pb collisions at
158A GeV. 0.05 0.1 0.15 0.2 x 10-2 100 200 300 400 - d (a) - d <Nw> B2 (GeV 2 c -3 ) 0.05 0.1 0.15 0.2 x 10-2 0 0.5 1 1.5 2 pt (GeV/c) B2 (GeV 2 c -3 ) (b)
FIG. 8. (Color online) Coalescence parameter B2 for d and d calculated from Eq. (3) in centrality selected Pb+ Pb col-lisions at 158A GeV. Centrality dependence is shown in (a),
ptdependence in (b).
for d shows little variation in the entire centrality range. This behavior can be understood as an indication of some degree of saturation in the density distribution of both nucleons and antinucleons achieved in midcentral Pb+ Pb collisions at the top SPS energy.
D. Coalescence
A combined analysis of the invariant yield spectra of composites and (anti)nucleons has been performed in the framework of a coalescence approach. This approach [16,17] relates the invariant yield of Z-charged A clusters (A denotes the atomic mass number and P the momentum) to the product of the yields of protons (p) and neutrons (n) as
EA d3NA d3P = BA Ep d3Np d3p Z En d3Nn d3p A−Z . (3)
TABLE III. Coalescence parameters B2as calculated from Eq.(3)
and averaged over the pt interval 0–0.9 GeV/c for d and d in
centrality selected Pb+ Pb collisions at 158A GeV in the rapidity interval−1.2 < y < −0.6. Errors are statistical only.
Centrality 0–12.5% 12.5–23.5% NW 315± 24 211± 19 B2(GeV2c−3) (7.5± 0.4) × 10−4 (11.4± 0.5) × 10−4 deuterons B2(GeV2c−3) (8.3± 1.1) × 10−4 (11.6± 2.0) × 10−4 antideuterons 044913-7
The (unmeasured) yield of neutrons is usually considered to be equal to that of protons; such an assumption seems quite reasonable at SPS energies [31]. Thermal models of cluster production [34,35] predict the coalescence parameter BAto be
inversely proportional to the volume of the particle source. Such models assume the same freeze-out conditions for matter and antimatter in chemical and thermal equilibrium. More advanced (hydrodynamically motivated) calculations, which implement collective expansion of the reaction zone within the density matrix approach [22] demonstrated a close relation of the characteristic (coalescence) radii to those obtained from two-particle correlation (HBT) analysis.
Since there is no overlap between the TOF acceptances for (anti)protons and (anti)deuterons [the rapidity coverage of the NA49 TOF detector at 158A GeV is −1.2 < y < −0.6 for d(d) and−0.5 < y < −0.1 for p(p)], the (anti)proton spectra measured by TOF were extrapolated to y= −0.9. The nor-malization scaling factors for the pt spectra were determined
using a Gaussian rapidity distribution for antiprotons and a parabolic function for protons. The function parameters were fitted to the experimental data [32]. The shape of the ptspectra,
however, remained unchanged; this assumption is based on the results of [32] which demonstrate that within|y| < 1 there is no significant variation in the transverse shape parameters of p(p) production.
In Fig. 8(a)(numerical values are given in TableIII) the coalescence factors B2 for d(d) as calculated from Eq. (3)
and averaged over the ptinterval 0–0.9 GeV/c are plotted as a
function ofNW for two centrality selected event samples. The
B2parameters for the A= 2 nuclei and antinuclei agree within
the errors; so the most likely conclusion is that the effective coalescence volumes for clusters and anticlusters are similar. The strong centrality dependence of B2 might be explained
as an increase of the transverse size of the source in more central collisions since in the centrality range under study B2
approximately scales inversely withNW.
The pt dependence of the calculated coalescence factors
B2 is plotted in Fig.8(b). We find no significant change for either d or d. This agrees with our previous measurements for d[13] but contradicts the rise reported in [36]. Comparing with
10-3 10-2 10 102
d
– √sNN(GeV) B - 2 (GeV 2 /c 3 ) Central collisions E864 Au+Pb NA44 Pb+Pb NA52 Pb+Pb NA49 Pb+Pb STAR Au+Au BRAHMS Au+Au PHENIX Au+AuFIG. 9. (Color online) Coalescence parameters B2for d in central A+ A interactions at different collision energies.
the calculations of Refs. [19,22], one is led to the conclusion that our results favor a Gaussian density profile of the source and an increase of the radial flow velocity∝ (r/R)αwith α in the range 0.5–1.0.
Our measurement of B2 along with other recent
experi-mental results on the coalescence parameter for antideuterons [37–41] is shown in Fig.9. Taking into account the variety of experimental conditions for the B2measurements (energy,
centrality and pt interval), the experimental data indicate that
there is no substantial decrease of the coalescence parameter in the region of √sN N from 17.3 to 200 GeV. This implies that the transverse size of the emitting source for d at kinetic
TABLE IV. Transverse momentum spectra d2N/(p
tdptdy) in GeV−2c2for deuterons in centrality selected Pb+ Pb collisions at 158A GeV
averaged over the rapidity interval−1.2 < y < −0.6.
pt 0–12.5% 12.5–23.5% 0–23.5% 0.10 (3.568± 0.13) × 10−1 (2.780± 0.12) × 10−1 (3.205± 0.12) × 10−1 0.30 (3.360± 0.97) × 10−1 (2.667± 0.089) × 10−1 (3.041± 0.093) × 10−1 0.50 (3.097± 0.12) × 10−1 (2.520± 0.11) × 10−1 (2.832± 0.11) × 10−1 0.70 (2.814± 0.15) × 10−1 (2.204± 0.14) × 10−1 (2.533± 0.14) × 10−1 0.90 (2.301± 0.13) × 10−1 (1.830± 0.12) × 10−1 (2.084± 0.12) × 10−1 1.10 (1.865± 0.11) × 10−1 (1.424± 0.095) × 10−1 (1.662± 0.10) × 10−1 1.30 (1.468± 0.11) × 10−1 (1.076± 0.090) × 10−1 (1.288± 0.10) × 10−1 1.50 (0.991± 0.085) × 10−1 (0.776± 0.081) × 10−1 (0.892± 0.083) × 10−1 1.70 (0.732± 0.076) × 10−1 (0.521± 0.066) × 10−1 (0.634± 0.072) × 10−1 1.90 (0.454± 0.057) × 10−1 (0.345± 0.053) × 10−1 (0.404± 0.055) × 10−1 2.10 (0.339± 0.053) × 10−1 (0.264± 0.045) × 10−1 (0.306± 0.049) × 10−1
ANTIDEUTERON AND DEUTERON PRODUCTION IN MID- . . . PHYSICAL REVIEW C 85, 044913 (2012) TABLE V. Transverse momentum spectra d2N/(p
tdptdy) in GeV−2c2 for antideuterons in centrality selected Pb+ Pb collisions at
158A GeV averaged over the rapidity interval−1.2 < y < −0.6.
pt 0–12.5% 12.5–23.5% 0–23.5%
0.075 (9.33± 2.5) × 10−4 (6.67± 2.4) × 10−4 (8.00± 1.7) × 10−4 0.225 (8.84± 1.8) × 10−4 (7.42± 1.8) × 10−4 (7.91± 1.3) × 10−4 0.375 (9.01± 2.2) × 10−4 (4.64± 1.6) × 10−4 (7.07± 1.4) × 10−4 0.675 (4.92± 1.9) × 10−4 (4.17± 2.0) × 10−4 (4.21± 1.4) × 10−4
freeze-out depends only weakly on √sN N in this energy domain.
V. SUMMARY
In this paper we present results on d and d production in the 23.5% most central Pb+ Pb collisions at 158A GeV. Antideuterons were measured in the rapidity range −1.2 < y <−0.6 and transverse momentum interval 0 < pt <
0.9 GeV/c. A qualitative comparison of the ptdistributions for
dand d showed close similarity of spectral shapes at all studied collision centralities. Thus no obvious effects of annihilation in the fireball medium were observed. The rapidity density normalized to the number of wounded nucleons exhibits no centrality dependence for either d or d. A difference was observed in the shapes of the rapidity distributions for d (convex) and d (concave). The 4π yields were estimated from a Gaussian and parabolic fit for d and d, respectively. The extracted coalescence parameters for d and d near midrapidity
TABLE VI. Transverse momentum spectra d2N/(p
tdptdy) in
GeV−2c2for protons in centrality selected Pb+ Pb collisions at 158A
GeV averaged over the rapidity interval−0.5 < y < −0.1.
pt 0–12.5% 12.5–23.5% 0–23.5% 0.05 (52.84± 0.90) (38.64± 0.54) (46.01± 0.73) 0.15 (50.74± 0.52) (36.82± 0.31) (44.04± 0.42) 0.25 (48.85± 0.48) (35.44± 0.29) (42.39± 0.39) 0.35 (44.41± 0.49) (31.19± 0.29) (38.05± 0.39) 0.45 (40.86± 0.49) (29.28± 0.29) (35.28± 0.39) 0.55 (37.11± 0.44) (26.06± 0.26) (31.79± 0.36) 0.65 (33.69± 0.40) (23.01± 0.23) (28.55± 0.32) 0.75 (28.19± 0.35) (18.69± 0.20) (23.62± 0.28) 0.85 (22.94± 0.30) (15.42± 0.18) (19.32± 0.24) 0.95 (17.72± 0.26) (12.09± 0.15) (15.01± 0.21) 1.05 (14.43± 0.22) (9.288± 0.15) (11.95± 0.18) 1.15 (11.12± 0.19) (7.138± 0.11) (9.205± 0.15) 1.25 (8.181± 0.16) (5.312± 0.089) (6.799± 0.12) 1.35 (5.874± 0.13) (3.950± 0.074) (4.947± 0.10) 1.45 (4.459± 0.11) (2.899± 0.061) (3.708± 0.086) 1.55 (3.083± 0.089) (1.901± 0.050) (2.557± 0.071) 1.65 (2.162± 0.079) (1.415± 0.045) (1.802± 0.063) 1.75 (1.535± 0.070) (1.028± 0.040) (1.291± 0.056) 1.85 (1.096± 0.064) (0.723± 0.036) (0.916± 0.050) 1.95 (0.749± 0.058) (0.477± 0.032) (0.618± 0.046) 2.05 (0.486± 0.051) (0.320± 0.029) (0.406± 0.040)
agree with each other within errors, implying a similar freeze-out configuration for matter and antimatter.
ACKNOWLEDGMENTS
This work was supported by the US Department of Energy Grant No. DE-FG03-97ER41020/A000, the Bundesministerium f¨ur Bildung und Forschung, Germany (06F 137), the Virtual Institute VI-146 of Helmholtz Gemeinschaft, Germany, the Polish Ministry of Science and Higher Education (1 P03B 006 30, 1 P03B 127 30, 0297/B/H03/2007/33, N N202 078735, N N202 078738, N N202 204638), the Hungarian Scientific Research Foundation (T032648, T032293, T043514), the Hungarian National Sci-ence Foundation, OTKA, (F034707), the Bulgarian National Science Fund (Ph-09/05), the Croatian Ministry of Science, Education and Sport (Project No. 098-0982887-2878) and Stichting FOM, the Netherlands.
APPENDIX
Tables IV, V, VI, and VII list the invariant transverse momentum spectra d2N/(p
tdptdy) in GeV−2c2 for d, d, p,
and p, respectively, in centrality selected Pb+ Pb collisions at 158A GeV.
TABLE VII. Transverse momentum spectra d2N/(p
tdptdy) in
GeV−2c2for antiprotons in centrality selected Pb+ Pb collisions at
158A GeV averaged over the rapidity interval−0.5 < y < −0.1.
pt 0–12.5% 12.5–23.5% 0–23.5% 0.05 (4.819± 0.24) (3.507± 0.15) (4.221± 0.20) 0.15 (4.548± 0.14) (3.323± 0.086) (3.991± 0.11) 0.25 (4.044± 0.12) (3.003± 0.074) (3.574± 0.097) 0.35 (3.694± 0.12) (2.654± 0.074) (3.223± 0.100) 0.45 (3.076± 0.11) (2.395± 0.071) (2.774± 0.094) 0.55 (2.743± 0.11) (2.054± 0.066) (2.434± 0.088) 0.65 (2.377± 0.099) (1.679± 0.059) (2.060± 0.079) 0.75 (1.871± 0.085) (1.377± 0.052) (1.649± 0.069) 0.85 (1.470± 0.074) (1.073± 0.045) (1.291± 0.060) 0.95 (1.226± 0.065) (0.833± 0.038) (1.046± 0.052) 1.05 (0.907± 0.056) (0.659± 0.033) (0.794± 0.045) 1.15 (0.743± 0.050) (0.500± 0.029) (0.632± 0.040) 1.25 (0.562± 0.045) (0.411± 0.027) (0.494± 0.037) 1.35 (0.401± 0.041) (0.304± 0.025) (0.358± 0.033) 1.45 (0.302± 0.038) (0.231± 0.024) (0.271± 0.031) 044913-9
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